There's actually a number of education historians who specialize in this field of study! I'm most familiar with American education but I'm happy to pass along some recommendations. Is there a particular aspect of history education you're interested in?

The history of history education is a fairly robust subfield with lots of great resources. The first bit of helpful context, though, is that "history class" is a fairly modern construct. I provide some history about the evolution of the subject here. And here, I explain why there's a difference in how history is taught in different states. Which is to say, the history of history class in Texas is different than the history in New York State.

However, a larger sense of the history of history education can be found in books that look at the history of curriculum. Tanner and Tanner's History of the School Curriculum is one of the foundational books on the topic, as is Kleibard's Struggle for the American Curriculum. That said, David Saxe provides a nice overview of the transition from "history" as seen in the 1893 Committee of Ten to the rise of "Social Studies" in Social Studies in Schools: A History of the Early Years. Which should be read with this piece, which is a good look at the historiography of the history of history education.